scholarly journals On the reciprocal degree distance of graphs

2012 ◽  
Vol 160 (7-8) ◽  
pp. 1152-1163 ◽  
Author(s):  
Hongbo Hua ◽  
Shenggui Zhang
Keyword(s):  
Degree Distance

WIENER POLYNOMIAL AND DEGREE DISTANCE POLYNOMIAL OF SOME GRAPHS

2020 ◽  
Vol 9 (9) ◽  
pp. 6863-6869
Author(s):  
D. Ahila Jeyanthi ◽  
T.M. Selvarajan
Keyword(s):  
Degree Distance

scholarly journals The minimum degree distance of graphs of given order and size

2008 ◽  
Vol 156 (18) ◽  
pp. 3518-3521 ◽  
Author(s):  
Orest Bucicovschi ◽  
Sebastian M. Cioabă
Keyword(s):  
Minimum Degree ◽  
Degree Distance

Reciprocal degree distance and graph properties

2019 ◽  
Vol 258 ◽  
pp. 1-7
Author(s):  
Mingqiang An ◽  
Yinan Zhang ◽  
Kinkar Ch. Das ◽  
Liming Xiong
Keyword(s):  
Graph Properties ◽  
Degree Distance

On eccentric distance sum and degree distance of graphs

2018 ◽  
Vol 250 ◽  
pp. 262-275 ◽  
Author(s):  
Hongbo Hua ◽  
Hongzhuan Wang ◽  
Xiaolan Hu
Keyword(s):  
Degree Distance ◽  
Eccentric Distance

scholarly journals Power-law distribution of degree–degree distance: A better representation of the scale-free property of complex networks

2020 ◽  
Vol 117 (26) ◽  
pp. 14812-14818 ◽  
Author(s):  
Bin Zhou ◽  
Xiangyi Meng ◽  
H. Eugene Stanley
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Power Law ◽  
Real World ◽  
Preferential Attachment ◽  
Statistical Tests ◽  
Finite Size ◽  
Distance Distribution ◽  
Scale Free ◽  
Degree Distance

Whether real-world complex networks are scale free or not has long been controversial. Recently, in Broido and Clauset [A. D. Broido, A. Clauset,Nat. Commun.10, 1017 (2019)], it was claimed that the degree distributions of real-world networks are rarely power law under statistical tests. Here, we attempt to address this issue by defining a fundamental property possessed by each link, the degree–degree distance, the distribution of which also shows signs of being power law by our empirical study. Surprisingly, although full-range statistical tests show that degree distributions are not often power law in real-world networks, we find that in more than half of the cases the degree–degree distance distributions can still be described by power laws. To explain these findings, we introduce a bidirectional preferential selection model where the link configuration is a randomly weighted, two-way selection process. The model does not always produce solid power-law distributions but predicts that the degree–degree distance distribution exhibits stronger power-law behavior than the degree distribution of a finite-size network, especially when the network is dense. We test the strength of our model and its predictive power by examining how real-world networks evolve into an overly dense stage and how the corresponding distributions change. We propose that being scale free is a property of a complex network that should be determined by its underlying mechanism (e.g., preferential attachment) rather than by apparent distribution statistics of finite size. We thus conclude that the degree–degree distance distribution better represents the scale-free property of a complex network.

On Steiner degree distance of trees

2016 ◽  
Vol 283 ◽  
pp. 163-167 ◽  
Author(s):  
Ivan Gutman
Keyword(s):  
Degree Distance
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